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Anisotropic Elastic Strain-Gradient Continuum from the Macro-Scale to the Granular Micro-Scale J. Elast. (IF 2.0) Pub Date : 2024-04-05 P. Pirmoradi, A. S. J. Suiker, P. Poorsolhjouy
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Identifying Second-Gradient Continuum Models in Particle-Based Materials with Pairwise Interactions Using Acoustic Tensor Methodology J. Elast. (IF 2.0) Pub Date : 2024-04-04 Gabriele La Valle, Christian Soize
This paper discusses wave propagation in unbounded particle-based materials described by a second-gradient continuum model, recently introduced by the authors, to provide an identification technique. The term particle-based materials denotes materials modeled as assemblies of particles, disregarding typical granular material properties such as contact topology, granulometry, grain sizes, and shapes
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Mid-Surface Scaling Invariance of Some Bending Strain Measures J. Elast. (IF 2.0) Pub Date : 2024-04-03
Abstract The mid-surface scaling invariance of bending strain measures proposed in (Int. J. Solids Struct. 37(39):5517–5528, 2000) is discussed in light of the work of (J. Elast. 146(1):83–141, 2021).
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Classical Elastodynamics as a Linear Symmetric Hyperbolic System in Terms of $({\mathbf{u}}_{\mathbf{x}}, {\mathbf{u}}_{t})$ J. Elast. (IF 2.0) Pub Date : 2024-04-03
Abstract Motivated from standard procedures in linear wave equations, we write the equations of classical elastodynamics as a linear symmetric hyperbolic system in terms of the displacement gradient ( \({\mathbf{u}}_{\mathbf{x}}\) ) and the velocity ( \({\mathbf{u}}_{t}\) ); this is in contrast with common practice, where the stress tensor and the velocity are used as the basic variables. We accomplish
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Existence and Exponential Decay for a Contact Problem Between Two Dissipative Beams J. Elast. (IF 2.0) Pub Date : 2024-04-03
Abstract We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is
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Complete Set of Bounds for the Technical Moduli in 3D Anisotropic Elasticity J. Elast. (IF 2.0) Pub Date : 2024-04-03
Abstract The paper addresses the problem of finding the necessary and sufficient conditions to be satisfied by the engineering moduli of an anisotropic material for the elastic energy to be positive for each state of strain or stress. The problem is solved first in the most general case of a triclinic material and then each possible case of elastic syngony is treated as a special case. The method of
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Inner and Outer Versions of Hyper-Elasticity J. Elast. (IF 2.0) Pub Date : 2024-04-03
Abstract Through suitable changes of variables for a typical problem in hyper-elasticity, either in the reference or deformed configurations, one can setup and analyze versions of the same problem in terms of inner or outer maps or variations. Though such kind of transformations are part of the classical background in the Calculus of Variations, we explore under what sets of hypotheses such versions
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Simulation of 3D Wave Propagation in Thermoelastic Anisotropic Media J. Elast. (IF 2.0) Pub Date : 2024-03-25 José M. Carcione, Enjiang Wang, Ayman N. Qadrouh, Mamdoh Alajmi, Jing Ba
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Plane Stress Problems for Isotropic Incompressible Hyperelastic Materials J. Elast. (IF 2.0) Pub Date : 2024-03-22 C. O. Horgan, J. G. Murphy
The analysis of plane stress problems has long been a topic of interest in linear elasticity. The corresponding problem for non-linearly elastic materials is considered here within the context of homogeneous incompressible isotropic elasticity. It is shown that when the problem is posed in terms of the Cauchy stress, a semi-inverse approach must be employed to obtain the displacement of a typical particle
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Negative Refraction of Mixing Waves in Nonlinear Elastic Wave Metamaterials J. Elast. (IF 2.0) Pub Date : 2024-03-22 Zi-Hao Miao, Yi-Ze Wang
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Angular Momentum in a Special Nonlinear Elastic Rod J. Elast. (IF 2.0) Pub Date : 2024-03-22 M. B. Rubin
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A Reformulation of the Browaeys and Chevrot Decomposition of Elastic Maps J. Elast. (IF 2.0) Pub Date : 2024-03-08 Walter Tape, Carl Tape
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Modelling the Deformation of Polydomain Liquid Crystal Elastomers as a State of Hyperelasticity J. Elast. (IF 2.0) Pub Date : 2024-02-26 Afshin Anssari-Benam, Zhengxuan Wei, Ruobing Bai
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A Strain Energy Function for Planar Response of a Constrained Cosserat Extensible Elastica with a General Reference Planar Shape J. Elast. (IF 2.0) Pub Date : 2024-02-21
Abstract An analytical expression for the strain energy of a constrained extensible Cosserat elastica is developed for general planar shapes and deformations of the rod. This strain energy function naturally couples tangential stretch and reference and current curvatures of the centroidal curve. The model considers a rigid rectangular cross-section of the rod which remains normal to the centroidal
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An Approximate Stress Distribution in a Conical Heap of Jammed Dry Granular Material J. Elast. (IF 2.0) Pub Date : 2024-02-20 M. B. Rubin
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Fiber-Reinforced Elastic Shells: A Direct Cosserat Approach J. Elast. (IF 2.0) Pub Date : 2024-02-19 Ryan C. McAvoy
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Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity J. Elast. (IF 2.0) Pub Date : 2024-02-13 Alireza Gharahi
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On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains J. Elast. (IF 2.0) Pub Date : 2024-02-05
Abstract Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation
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Internally Balanced Elasticity Tensor in Terms of Principal Stretches J. Elast. (IF 2.0) Pub Date : 2024-02-05 Ashraf Hadoush
A new scheme for hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. Then, Piola–Kirchhoff stress is coupled with internal balance equation. Strain energy function is expressed in terms of principal invariants of the deformation gradient decomposed counterparts. Recent work introduces a strain
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Pure Torsion for Stretch-Based Constitutive Models for Incompressible Isotropic Hyperelastic Soft Materials J. Elast. (IF 2.0) Pub Date : 2024-01-25 Cornelius O. Horgan
Stretch-based constitutive models for isotropic hyperelastic materials as alternatives to the classical strain invariant models have been the subject of considerable recent attention largely motivated by application to modelling the mechanical response of soft tissues. One such four-parameter constitutive model was proposed recently by Anssari-Benam (J. Elast. 153:219–244, 2023) for incompressible
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Potential Functions for Functionally Graded Transversely Isotropic Media Subjected to Thermal Source in Thermoelastodynamics Problems J. Elast. (IF 2.0) Pub Date : 2024-01-24
Abstract This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study
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Revisiting Stress Propagation in a Two-Dimensional Elastic Circular Disk Under Diametric Loading J. Elast. (IF 2.0) Pub Date : 2024-01-10 Yosuke Sato, Haruto Ishikawa, Satoshi Takada
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A Novel Approach to Setting the Problem of Lagrange for Dynamical Systems and Nonlinear Elastodynamics J. Elast. (IF 2.0) Pub Date : 2024-01-09
Abstract The classical Lagrange problem for dynamical systems introduces a Lagrangian action functional defined for any dynamical process that is envisioned to take place over a fixed interval of time with its state at each time lying on an unknown, but prescribed, configuration between two given end points in an \(n\) -dimensional state space \(\mathbb{R}^{n}\) . It is proposed that the fundamental
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Scholarly Works, Academic Lineage, and Doctoral Advisees of Jerald L. Ericksen J. Elast. (IF 2.0) Pub Date : 2024-01-03 Roger Fosdick, Eliot Fried, Chi-Sing Man
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The Euler–Bernoulli Limit of Thin Brittle Linearized Elastic Beams J. Elast. (IF 2.0) Pub Date : 2023-11-28 Janusz Ginster, Peter Gladbach
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Complete General Solutions for Equilibrium Equations of Isotropic Strain Gradient Elasticity J. Elast. (IF 2.0) Pub Date : 2023-11-24 Yury Solyaev
In this paper, we consider isotropic Mindlin–Toupin strain gradient elasticity theory, in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory, we developed an extended form of Boussinesq–Galerkin (BG) and Papkovich–Neuber (PN) general solutions. The obtained form of BG solution allows to define the displacement field through a single
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Controllable Deformations of Unconstrained Ideal Nematic Elastomers J. Elast. (IF 2.0) Pub Date : 2023-10-18 L. Angela Mihai, Alain Goriely
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On the Question of the Sign of Size Effects in the Elastic Behavior of Foams J. Elast. (IF 2.0) Pub Date : 2023-10-06 Stephan Kirchhof, Alfons Ams, Geralf Hütter
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A Generalized Model for Large Deformations of an Elastically Isotropic Material with Elastic-Inelastic Response J. Elast. (IF 2.0) Pub Date : 2023-09-13 M. B. Rubin
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Cauchy Relations in Linear Elasticity: Algebraic and Physics Aspects J. Elast. (IF 2.0) Pub Date : 2023-09-07 Yakov Itin
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Edge Crack Subject to Anti-Plane Shear Wave in an Orthotropic Strip J. Elast. (IF 2.0) Pub Date : 2023-08-28 Somashri Karan, Sourav Kumar Panja, Sanjoy Basu, Subhas Chandra Mandal
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Construction of Invariant Relations of $n$ Symmetric Second-Order Tensors J. Elast. (IF 2.0) Pub Date : 2023-08-28 Adair Roberto Aguiar, Gabriel Lopes da Rocha
A methodology is presented to find either implicit or explicit relations, called syzygies, between invariants in a minimal integrity basis for \(n\) symmetric second-order tensors defined on a three-dimensional euclidean space. The methodology i) yields explicit non-polynomial expressions for certain invariants in terms of the remaining invariants in the integrity basis and ii) allows the construction
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Foreword: In Recognition of the 85th Birthday of Roger L. Fosdick J. Elast. (IF 2.0) Pub Date : 2023-08-25 Ryan S. Elliott, Adair R. Aguiar, Yi-Chao Chen, Gianni Royer-Carfangi
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Decomposition of Rod Displacements via Bernoulli–Navier Displacements. Application: A Loading of the Rod with Shearing J. Elast. (IF 2.0) Pub Date : 2023-08-04 Georges Griso
Within the framework of linear elasticity, we show that any displacement of a straight rod is the sum of a Bernoulli–Navier displacement and two terms, one for shearing and the other for warping. Then, we load a straight rod so that bending and shear contribute the same to the rotations of the cross-section.
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A Class of Nonlinear Elasticity Problems with No Local but Many Global Minimizers J. Elast. (IF 2.0) Pub Date : 2023-08-04 Yury Grabovsky, Lev Truskinovsky
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Stress Concentration Due to the Presence of a Rigid Elliptical Inclusion in Porous Elastic Solids Described by a New Class of Constitutive Relations J. Elast. (IF 2.0) Pub Date : 2023-07-21 Bhaskar Vajipeyajula, Pavitra Murru, K. R. Rajagopal
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Anisotropy and Asymmetry of the Elastic Tensor of Lattice Materials J. Elast. (IF 2.0) Pub Date : 2023-07-18 Huiming Yin, Chao Liu
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Ericksen-Landau Modular Strain Energies for Reconstructive Phase Transformations in 2D Crystals J. Elast. (IF 2.0) Pub Date : 2023-07-13 Edoardo Arbib, Paolo Biscari, Clara Patriarca, Giovanni Zanzotto
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Inclusions with Uniform Stress in a Bounded Elastic Domain J. Elast. (IF 2.0) Pub Date : 2023-07-07 Ming Dai
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Solid Phase Transitions in the Liquid Limit J. Elast. (IF 2.0) Pub Date : 2023-06-21 Yury Grabovsky, Lev Truskinovsky
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Universal Deformations of Incompressible Nonlinear Elasticity as Applied to Ideal Liquid Crystal Elastomers J. Elast. (IF 2.0) Pub Date : 2023-06-07 Victoria Lee, Kaushik Bhattacharya
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Singular Points and Singular Curves in von Kármán Elastic Surfaces J. Elast. (IF 2.0) Pub Date : 2023-06-06 Animesh Pandey, Anurag Gupta
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Nucleation and Development of Multiple Cracks in Thin Composite Fibers via the Inverse-Deformation Approach J. Elast. (IF 2.0) Pub Date : 2023-06-06 Arnav Gupta, Timothy J. Healey
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A Second Gradient Theory of Thermoelasticity J. Elast. (IF 2.0) Pub Date : 2023-05-22 D. Ieşan, R. Quintanilla
This paper is concerned with a linear theory of thermoelasticity without energy dissipation, where the second gradient of displacement and the second gradient of the thermal displacement are included in the set of independent constitutive variables. In particular, in the case of rigid heat conductors the present theory leads to a fourth order equation for temperature. First, the basic equations of
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Renormalized Energy of a Dislocation Loop in a 3D Anisotropic Body J. Elast. (IF 2.0) Pub Date : 2023-05-09 Miroslav Šilhavý
The paper presents a rigorous analysis of the singularities of elastic fields near a dislocation loop in a body of arbitrary material symmetry that extends over the entire three-space. Explicit asymptotic formulas are given for the stress, strain and the incompatible distortion near the curved dislocation. These formulas are used to analyze the main object of the paper, the renormalized energy. The
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Damage as a Material Phase Transition J. Elast. (IF 2.0) Pub Date : 2023-04-26 Andrea Bucchi, Domenico De Tommasi, Giuseppe Puglisi, Giuseppe Saccomandi
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Relaxation and Domain Wall Structure of Bilayer Moiré Systems J. Elast. (IF 2.0) Pub Date : 2023-04-25 Paul Cazeaux, Drake Clark, Rebecca Engelke, Philip Kim, Mitchell Luskin
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Mechanical Response of Metal Solenoids Subjected to Electric Currents J. Elast. (IF 2.0) Pub Date : 2023-04-25 R. S. Elliott, N. Triantafyllidis
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A Double Coated Circular Inhomogeneity Neutral to an Arbitrary Uniform in-Plane Stress Field J. Elast. (IF 2.0) Pub Date : 2023-04-19 Xu Wang, Peter Schiavone
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On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation J. Elast. (IF 2.0) Pub Date : 2023-04-18 Angkana Rüland, Theresa M. Simon
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Harmonic Decomposition, Irreducible Basis Tensors, and Minimal Representations of Material Tensors and Pseudotensors J. Elast. (IF 2.0) Pub Date : 2023-04-11 Chi-Sing Man, Wenwen Du
We propose a general and efficient method to derive various minimal representations of material tensors or pseudotensors for crystals. By a minimal representation we mean one that pertains to a specific Cartesian coordinate system under which the number of independent components in the representation is the smallest possible. The proposed method is based on the harmonic and Cartan decompositions and
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Stable Möbius Bands from Isometrically Deformed Circular Helicoids J. Elast. (IF 2.0) Pub Date : 2023-03-21 Vikash Chaurasia, Eliot Fried
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Gels: Energetics, Singularities, and Cavitation J. Elast. (IF 2.0) Pub Date : 2023-03-21 M. Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song
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A New Drucker Yield Function for Orthorhombic Aggregates of Cubic Crystallites J. Elast. (IF 2.0) Pub Date : 2023-03-21 Mojia Huang, Fengying Xiao, Zhiwen Lan
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A Variational Derivation of Stoney-Like Formulas for Self-Stressed Bilayered Plates J. Elast. (IF 2.0) Pub Date : 2023-03-21 Antonio DiCarlo, Roberto Paroni, Raffaella Rizzoni
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Perturbation of Bleustein–Gulyaev Waves in Piezoelectric Media: Barnett and Lothe Integral Formalism Revisited J. Elast. (IF 2.0) Pub Date : 2023-03-17 Kazumi Tanuma, Xiang Xu, Gen Nakamura
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On the Algebraic Riccati Equations of Finite Elastostatics J. Elast. (IF 2.0) Pub Date : 2023-03-15 Gearoid Mac Sithigh
In the setting of either compressible or incompressible Finite Elastostatics, Agmon’s condition may be formulated in terms of an algebraic Riccati equation. These equations are studied under the assumption of Strong Ellipticity.
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Radially Oscillating Incompressible Hyperelastic Multi-Layer Tubes: Interface Effects and Energy Approach J. Elast. (IF 2.0) Pub Date : 2023-03-15 Atacan Yucesoy, Thomas J. Pence